Wednesday, March 28, 2012

The Joker Effect, Batman, and Game Theory.

The Joker, as envisioned by Doug Mahnke.  Source.


I am not entirely certain how many times I will ever say this, but I stumbled across a truly fascinating paper in the Journal of Theoretical Biology (thanks, Reddit!) recently, and would like to share the results as best I can.  Not being a theoretical biologist or an avid practitioner of game theory, my understanding may be somewhat limited, but it is exciting nonetheless.

To begin, I will explain game theory as best I can (having background in neither biology nor economics, and having been awake for 23 hours at this point).  Game theory was originally envisioned as a tool for economics.  This predictive mechanism assumes that complicated, real-world situations may be reduced to a "game", a situation with clear rules and rewards.  I have heard through my travels, conversation and the Colbert Report that game theory has been used to predict elections, the collapse of the Soviet Union and various other seemingly unpredictable events.  In an interesting twist, it became clear to scientists that not only could the theory be used for economics, but [bizarrely] seemed to fit biological systems perhaps better than those for which it was designed.

In order to effectively model biological systems and how populations could grow and change over time, evolutionary game theory was developed.  In this system:

1.  A population is considered.
2.  The individuals' strategies are evaluated according to the "rules" of the game.  These individuals are then assigned a fitness (this fitness function is not unlike that present in genetic algorithms).
3.  The fitness of the individuals are considered, and the population increases by one, the new individual likely being a member of the fittest group.  An individual could also change strategies, rather than adding another.
4.  This new population goes back to step 1.

Thus, successful "players" will become increasingly significant in terms of the population, and less successful players will be overtaken.  The paper by Arenas et al. [J. Theor. Bio., 279 (2011) 113-119] utilises this in order to evaluate the performance of individuals in the game.

The game considered is known as a public good game.  There exists a value for the public good, and there are at least two player types in these games.  Cooperators contribute to the public good at some cost to themselves, while defectors are free-riders.  They consume public good while contributing nothing.  You could think of them as taxpayers and non-taxpayers.  With only these two players, defectors often overtake cooperators, a straightforward result since the defectors are not at all burdened. However, the real world, and most real systems are not this simple.  It is assumed that this is due to the presence of other players.

Batman, the ultimate cooperator. Source.
Here, we introduce the Joker.  Where we may consider the Batman to be the ultimate cooperator (great contributions to the public good at tremendous self-cost), and corrupt officials/organized criminals to be defectors, we may introduce a character which introduces new and interesting dynamics.  The Joker, as in his universe, does not personally consume public good, nor does he contribute to it.  However, he destroys large chunks of public good because some men want to watch the world burn.  The introduction of a Joker character over the course of a full simulation can lead to one of two ultimate scenarios.  In the event that Jokers are wildly successful and/or effective, they will overtake the simulation leaving only chaos and anarchy in their wake.  Since this does not appear to happen (either in the Batman universe, or ours), it would appear the scenarios leading to this eventuality are based upon poor assumptions.
The alternative result is that which would more closely mirror reality.  Here, it is assumed that Jokers will never fully overtake cooperators.  This is due to the fact that cooperators thrive off the public good they produce, ensuring at least a small population of them at any given time.  Let me attempt to describe what would happen to a cooperator-defector game with the introduction of a Joker.

1.  As stated above, defectors outnumber cooperators.  This drain on the public good is ultimately detrimental to all parties.
2.  The Joker is introduced.  The threat to the public good makes defectors ultimately unsustainable, and their population share crashes.
3.  A small group of cooperators survives, doing very well on an individual basis (i.e. high fitness), this leads to expansion of their population share.
4. The increase in cooperators leads to an increase in public good, which allows for defectors to emerge from the woodwork, and begin to claim population share at the expense of cooperators.
5.  Repeat.

This scenario ultimately avoids the cooperators being crushed/exploited by the defectors.  In the end, cooperators do much better than they would without a Joker.  As an interesting note, this scenario has been documented in nature.  In the presence of predators, cooperation is actively encouraged where it would not exist otherwise.  Picture a flock of smaller birds chasing away a raptor, even where they would not cooperate otherwise.  Even in humans, it seems that only through the presence of destructive agents (common enemies, perhaps) that we can disregard our differences and get along.

I shall now leave the question that was ultimately posed by the paper.  Who is the true saviour of Gotham City?  Is it Batman, or the Joker?


P.S.  Please point out any grammar/spelling/logic errors.  Proof reading takes time and effort, and I'm going to bed.
P.P.S Edited 2012/07/28, finally gave it a once over.  Also, if I ever become a supervillian, I'll model myself after the Joker.  You know, for the greater good.

Monday, March 12, 2012


A Canadian $1 coin, for those of you unfamiliar. Source.


I recently learned about a study performed by the Canadian government in the 1970s which is incredibly interesting and yet comparatively unknown.  Information appears to be sparse, but I wish to tell you what I've found.  It's rather interesting, and could have dramatic positive consequences.  The best I think I can do for now is to link you to the Wikipedia article, which I assume will grow and change as more information is published.

Mincome is the name of a project set in motion by the governments of Canada and Manitoba.  The objective to see what consequences a guaranteed annual income (GAI) would have on a given workforce.  The payment of the GAI would be reduced by some fraction for every dollar earned by a family.  It was assumed, I would say fairly, that without a pressing economic incentive to work, many people would simply choose not to do so.  However, this is why we experiment, for hypotheses are still just guesses.

While some families were offered the GAI payments in larger urban centers like Winnipeg, one site was chosen as an "isolated" experiment.  This was the town of Dauphin, Manitoba.  All ten thousand people, including seniors and those unable to work, were offered a GAI.  This strict universality was key to the experiment, as nationwide GAI policies had been suggested beginning in 1971.  It would seem that theoretical examinations had suggested GAI would be beneficial to a nation struggling with poverty.  The project began around 1974 and continued to 1979, when funding was cut due to a pressing economic crisis.

The results were interesting, to say the least.  First however, think about this for a moment.  If you were guaranteed not a good, but a living wage to do nothing, what would you do?  If the results from Dauphin are to be believed, around 98% of you would choose to work.  The male workforce shrank by a mere 1%, along with reductions of 3% for wives, and 5% for unmarried women.  However, these numbers are not just uniform reductions.  This was a time when secondary school diplomas were not as widespread as they are today.  In rural communities where labour was required on the farm, teenage boys would often choose the farm over grade 12 due to financial concerns.  Married women which left the workforce often did so when a child was born.  This departure from the workforce was not permanent as far as I know, but women did choose to stay at home longer with their child or children.

It is also important to note that a host of benefits resulted from the GAI experiment.  Health care costs were reduced by 8.5%.  One article on the subject (to which I have lost the link), mentioned that a large fraction of hospital visits could be considered medical consequences of poverty.  This was in part due to a reduction in work related accidents, fewer car accidents and fewer instances of domestic abuse.  It has also been speculated that without the economic disincentives, people who were sick would choose to recover more completely before returning to work.  I would also hazard a guess that a host of stress-related illnesses decreased, but I can only guess.

After the project's cancellation in 1979, the information was gathered together, boxed up, and not considered again until relatively recently.  It would seem that the GAI experiment resulted in a happier and healthier workforce.  My [limited] knowledge of psychology would suggest that this results in higher quality work and lower crime rates.  I certainly look forward to learning the results of the detailed reviews of the data.  And frankly, I think the social and economic benefits could potentially outweigh the costs, particularly when Canada pays for the health care of its citizens.


P.S.  I've been working 12 hour night shifts, and haven't the time for proof-reading.  Please be kind.

One Thousand Views.

A picture of the aftermath of the Tunguska event, an explosion resulting from a meteorite or comet hitting Earth.  Source.

To you, my non-spambot, monocled followers, I offer sincere thanks.  My blog has reached over a thousand pageviews.

Though I am now gainfully employed, it would seem that my last [surprisingly busy] month of unemployment was certainly not fertile ground for blogging.  I have also hit a wall in which I have run out of things to talk about that:

1) I know enough about to write an informative blog post, and;

2) I think people would actually be interested in reading.

My blog, lacking of a clear vision and direction, will [hopefully] continue to inform on topics I find interesting (though will likely be less exhaustive), update on developments in previous blog topics, and present absurdly long, detailed arguments for opinions which I hold (now that you know how I feel about beards and Sens Army).  In lieu of an informative blog post, please accept the link in the caption of the above picture, because who wouldn't want to learn about an unexplained explosion?

Spam-bots, that's who.